Electronic properties of the coronene series from thermally-assisted-occupation density functional theory

Abstract

To fully utilize the great potential of graphene in electronics, a comprehensive understanding of the electronic properties of finite-size graphene flakes is essential. While the coronene series with n fused benzene rings at each side (designated as n-coronenes) are possible structures for opening a band gap in graphene, their electronic properties are not yet fully understood. Nevertheless, because of their radical character, it remains very difficult to reliably predict the electronic properties of the larger n-coronenes with conventional computational approaches. In order to circumvent this, the various electronic properties of n-coronenes (n = 2-11) are investigated using thermally-assisted-occupation density functional theory (TAO-DFT) [J.-D. Chai, J. Chem. Phys., 2012, 136, 154104], a very efficient electronic structure method for studying nanoscale systems with strong static correlation effects. The ground states of the larger n-coronenes are shown to be polyradical singlets, where the active orbitals are mainly localized at the zigzag edges.

Fig. 1. Structure of n-coronene, containing n fused benzene rings at each side.

Fig. 2. Singlet–triplet energy gap of n-coronene (left: n = 2–11; right: n = 6–11), obtained with spin-unrestricted TAO-LDA, KS-LDA, and KS-B3LYP. Here, the experimental data is taken from the literature.

Fig. 3. (a) Vertical ionization potential, (b) vertical electron affinity, and (c) fundamental gap for the lowest singlet state of n-coronene, obtained with spin-unrestricted TAO-LDA. Here, the experimental data are taken from the literature.

Fig. 4. Symmetrized von Neumann entropy for the lowest singlet state of n-coronene, obtained with spin-restricted TAO-LDA.

Fig. 5. Active orbital occupation numbers (HOMO−8, …, HOMO−1, HOMO, LUMO, LUMO+1, …, and LUMO+8) for the lowest singlet state of n-coronene, obtained with spin-restricted TAO-LDA. For brevity, HOMO is denoted as H, LUMO is denoted as L, and so on.

Fig. 6. Real-space representation of the HOMO−1 (1.988), HOMO (1.988), LUMO (0.012), and LUMO+1 (0.012) for the lowest singlet state of 3-coronene, obtained with spin-restricted TAO-LDA, at isovalue = 0.01 e Å⁻³. The orbital occupation numbers are given in parentheses.

Fig. 7. Real-space representation of the HOMO−1 (1.865), HOMO (1.864), LUMO (0.136), and LUMO+1 (0.136) for the lowest singlet state of 5-coronene, obtained with spin-restricted TAO-LDA, at isovalue = 0.01 e Å⁻³. The orbital occupation numbers are given in parentheses.

Fig. 8. Real-space representation of the HOMO−1 (1.602), HOMO (1.601), LUMO (0.411), and LUMO+1 (0.409) for the lowest singlet state of 7-coronene, obtained with spin-restricted TAO-LDA, at isovalue = 0.01 e Å⁻³. The orbital occupation numbers are given in parentheses.

Fig. 9. Real-space representation of the HOMO−1 (1.353), HOMO (1.352), LUMO (0.685), and LUMO+1 (0.684) for the lowest singlet state of 9-coronene, obtained with spin-restricted TAO-LDA, at isovalue = 0.01 e Å⁻³. The orbital occupation numbers are given in parentheses.